Finite Group Databasebeta

#124×#1057 #16800253

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct product#124×#1057

Splittings

SylowC13 ⋊ C8×#124

Subgroups

subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C23×C8
FittingC2×C13×#124C4
socleC23×C13C23×C4
prime radicalC22×D4×C13C2×C4
cosocleC22×Dic13C24
hypercenterC2×#124#261
hypocenterC13C8×#124
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#124

974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1106902);